Why projection system is used in GIS?

to represent the 3-dimensional surface of the earth or other round body on a 2-dimensional plane in cartography

Projection is how the 3D earth is mapped on a 2D planar surface (paper map or digital GIS). All projections have some error, but each differs in the type of error. Listed below are projection characteristics: 

Conformality, or “Conformal” projections o Preserves shape. o When the scale of a map at any point on the map is the same in any direction, the projection is conformal. Meridians (lines of longitude) and parallels (lines of latitude) intersect at right angles. • Area, or “Equivalent” projections o Preserves area. o When a map portrays areas over the entire map so that all mapped areas have the same proportional relationship to the areas on the Earth that they represent, the map is an equal-area, or equivalent, map. • Distance o A map is equidistant when it portrays distances from the center of the projection to any other place on the map. • Direction o A map preserves direction when azimuths (angles from a point on a line to another point) are portrayed correctly in all directions.

Coordinate systems enable geographic datasets to use common locations for integration. A coordinate system is a reference system used to represent the locations of geographic features, imagery, and observations, such as Global Positioning System (GPS) locations, within a common geographic framework.

A datum typically defines the surface (ex radius for a sphere, major axis and minor axis or inverse flattening for an ellipsoid) and the position of the surface relative to the center of the earth.